The spin-forbidden absorption spectrum of Fe2+ in orthopyroxene

In this article, we have established the energy matrices of the strong-field terms SΓ of the d ⁴ (d ⁶) electron configuration in a crystal-field with C _2v symmetry. When we used this procedure to calculate the spin-forbidden absorption bands of Fe²⁺ in the M(2) site in orthopyroxene, we substituted the single-electron crystal-field energy levels (determined by the experimental results of the spinallowed spectrum) into the energy matrices instead of the single-electron crystal-field matrix elements. Thus, by means of only one parameter B (C=4B), most of the spin-forbidden bands of Fe²⁺ have been determined. Furthermore, when a similar treatment was made of the M(1) site of O _h symmetry, the entire spin-forbidden spectrum of Fe²⁺ in orthopyroxenes could be semiquantitatively explained. This shows that the method is particularly useful for the calculation of spin-forbidden spectra of complexes with the d ⁴ (d ⁶) configuration in a low-symmetry site.     

Electronic absorption and luminescence spectroscopic studies of kyanite single crystals: differentiation between excitation of FeTi charge transfer and Cr3+ dd transitions

A selected set of five different kyanite samples was analysed by electron microprobe and found to contain chromium between <0.001 and 0.055 per formula unit (pfu). Polarized electronic absorption spectroscopy on oriented single crystals, R₁, R₂-sharp line luminescence and spectra of excitation of λ₃- and λ₄-components of R₁-line of Cr³⁺-emission had the following results: (1) The Fe²⁺–Ti⁴⁺ charge transfer in c-parallel chains of edge connected M(1) and M(2) octahedra shows up in the electronic absorption spectra as an almost exclusively c(||Z′)-polarized, very strong and broad band at 16000 cm⁻¹ if <, in this case the only band in the spectrum, and at an invariably lower energy of 15400 cm⁻¹ in crystals with  ≥ . The energy difference is explained by an expansion of the O_f–O_k, and O_b–O_m edges, by which the M(1) and M(2) octahedra are interconnected (Burnham 1963), when Cr³⁺ substitutes for Al compared to the chromium-free case. (2) The Cr³⁺ is proven in two greatly differing crystal fields a and b, giving rise to two sets of bands, derived from the well known dd transitions of Cr^{3+ 4}A_2g→⁴T_2g(F)(I), →⁴T_1g(F)(II), and →⁴T_1g(P)(III). Band energies in the two sets a and b, as obtained by absorption, A, and excitation, E, agree well: I: 17300(a, A), 17200(a, E), 16000(b, A), 16200(b, E); II: 24800(a, A), 24400(a, E); 22300(b, A), 22200(b, E); III: 28800(b,A) cm⁻¹. Evaluation of crystal field parameters from the bands in the electronic spectra yield Dq(a)=1730 cm⁻¹, Dq(b)=1600 cm⁻¹, B(a)=790 cm⁻¹, B(b)=620 cm⁻¹ (errors ca. ±10 cm⁻¹), again in agreement with values extracted from the λ³, λ⁴ excitation spectra. The CF-values of set a are close to those typical of Cr³⁺ substituting for Al in octahedra of other silicate minerals without constitutional OH⁻ as for sapphirine, mantle garnets or beryl, and are, therefore, interpreted as caused by Cr³⁺ substituting for Al in some or all of the M(1) to M(4) octaheda of the kyanite structure, which are crystallographically different but close in their mean Al–O distances, ranging from 1.896 to 1.919 A (Burnham 1963), and slight degrees of distortion. Hence, band set a originates from substitutive Cr³⁺ in the kyanite structural matrix. The CF-data of Cr³⁺ type b, expecially B, resemble those of Cr³⁺ in oxides, especially of corundum type solid solutions or eskolaite. This may be interpreted by the assumption that a fraction of the total chromium contents might be allocated in a precursor of a corundum type exsolution. Received: 3 January 1997 / Revised, accepted: 2 May 1997     

EPR study of coordination of Ag and Pb cations in BaB<Subscript>2</Subscript>O<Subscript>4</Subscript> crystals and barium borate glasses

It is shown the possibility to determine the coordination of paramagnetic ions in disordered solid structures, e.g., in barium borate glasses. For this purpose the electron paramagnetic resonance (EPR) method was used to study α-and β-BaB₂O₄ crystals and glasses of 45·BaO × 55·B₂O₃ and 40·BaO × 60·B₂O₃ (mol%) composition activated by Ag⁺ and Pb²⁺ ions. After the samples were exposed to X-rays at 77 K, different EPR centers were observed in them. In α-and β-BaB₂O₄ crystals and glasses the EPR centers Ag²⁺, Ag⁰, Pb⁺, Pb³⁺, and hole centers of O⁻ type were studied. The EPR parameters of these centers and their arrangement in crystal structure were determined. It is shown that Pb³⁺ ions in β-BaB₂O₄ crystals occupy Ba²⁺ position in an irregular polyhedron from the eight oxygen, whereas in α-BaB₂O₄ crystals they occupy Bа₂ position in a sixfold coordination. Pb⁺ ions in α-BaB₂O₄ crystals occupy Bа₁ position in a ninefold coordination from oxygen. In barium borate glasses, Pb³⁺ ions were studied in coordination polyhedron from six oxygen atoms and in a polyhedron from nine to ten oxygen atoms. It is assumed that the established difference in the structural position of Pb³⁺ ions in glasses is due to their previous incorporation in associative cation–anion complexes (AC) and “free” structure-forming cations (FC). Computer simulations have been performed to analyze the stability of specific associative complexes and to compare their bond lengths with experimental data.     

Calculations of crystal-field spectra of Cu2+ ions in some low-symmetry minerals

The expressions of the crystal-field potential energies and perturbation matrix elements corresponding to the point symmetriesC _4v ,D _2h andC _i are given in this paper. The crystal-field transition frequencies of Cu²⁺ ions in metatorbernite, conichalcite and turquoise calculated by using these expressions are also reported. The calculated results are essentially consistent with experimental data.     

Synthetic and natural chromium-bearing spinels: an optical spectroscopy study

Four samples of synthetic chromium-bearing spinels of (Mg, Fe²⁺)(Cr, Fe³⁺)₂O₄ composition and four samples of natural spinels of predominantly (Mg, Fe²⁺)(Al, Cr)₂O₄ composition were studied at ambient conditions by means of optical absorption spectroscopy. Synthetic end-member MgCr₂O₄ spinel was also studied at pressures up to ca. 10 GPa. In both synthetic and natural samples, chromium is present predominantly as octahedral Cr³⁺ seen in the spectra as two broad intense absorption bands in the visible range caused by the electronic spin-allowed ⁴ A _2g  → ⁴ T _2g and ⁴ A _2g  → ⁴ T _1g transitions (U- and Y-band, respectively). A distinct doublet structure of the Y-band in both synthetic and natural spinels is related to trigonal distortion of the octahedral site in the spinel structure. A small, if any, splitting of the U-band can only be resolved at curve-fitting analysis. In all synthetic high-chromium spinels, a couple of relatively narrow and weak bands of the spin-allowed transitions ⁴ A _2g  → ² E _g and ⁴ A _2g  → ² T _1g of Cr³⁺, intensified by exchange-coupled interaction between Cr³⁺ and Fe³⁺ at neighboring octahedral sites of the structure, appear at ~14,400 and ~15,100 cm^?1. A vague broad band in the range from ca. 15,000 to 12,000 cm^?1 in synthetic spinels is tentatively attributed to ^IVCr²⁺ + ^VICr³⁺ → ^IVCr³⁺ + ^VICr²⁺ intervalence charge-transfer transition. Iron, mainly as octahedral Fe³⁺, causes intense high-energy absorption edge in near UV-range (ligand–metal charge-transfer O^2? → Fe³⁺, Fe²⁺ transitions). As tetrahedral Fe²⁺, it appears as a strong infrared absorption band at around 4,850 cm^?1 caused by electronic spin-allowed ⁵ E → ⁵ T ₂ transitions of ^IVFe²⁺. From the composition shift of the U-band in natural and synthetic MgCr₂O₄ spinels, the coefficient of local structural relaxation around Cr³⁺ in spinel MgAl₂O₄–MgCr₂O₄ system was evaluated as ~0.56(4), one of the lowest among (Al, Cr)O₆ polyhedra known so far. The octahedral modulus of Cr³⁺ in MgCr₂O₄, derived from pressure-induced shift of the U-band of Cr³⁺, is ~313 (50) GPa, which is nearly the same as in natural low-chromium Mg, Al-spinel reported by Langer et al. (1997). Calculated from the results of the curve-fitting analysis, the Racah parameter B of Cr³⁺ in natural and synthetic MgCr₂O₄ spinels indicates that Cr–O-bonding in octahedral sites of MgCr₂O₄ has more covalent character than in the diluted natural samples. Within the uncertainty of determination in synthetic MgAl₂O₄ spinel, B does not much depend on pressure.     

Electric conductivity of Fe2SiO4–Fe3O4 spinel solid solutions

 The spinel solid solution was found to exist in the whole range between Fe₃O₄ and γ-Fe₂SiO₄ at over 10 GPa. The resistivity of Fe_{3− x} Si _x O₄ (0.0<x<0.288) was measured in the temperature range of 80∼300 K by the AC impedance method. Electron hopping between Fe³⁺ and Fe²⁺ in the octahedral site of iron-rich phases gives a large electric conductivity at room temperature. The activation energy of the electron hopping becomes larger with increasing γ-Fe₂SiO₄ component. A nonlinear change in electric conductivity is not simply caused by the statistical probability of Fe³⁺–Fe²⁺ electron hopping with increasing the total Si content. This is probably because a large number of Si⁴⁺ ions occupies the octahedral site and the adjacent Fe²⁺ keeping the local electric neutrality around Si⁴⁺ makes a cluster, which generates a local deformation by Si substitution. The temperature dependence of the conductivity of solid solutions indicates the Verwey transition temperature, which decreases from 124(±2) K at x=0 (Fe₃O₄) to 102(±5) K at x=0.288, and the electric conductivity gap at the transition temperature decreases with Si⁴⁺ substitution. Received: 15 March 2000 / Accepted: 4 September 2000     

From the green color of eskolaite to the red color of ruby: an X-ray absorption spectroscopy study

The best known cause for colors in insulating minerals is due to transition metal ions as impurities. As an example, Cr³⁺ is responsible for the red color of ruby (α-Al₂O₃:Cr³⁺) and the green color of eskolaite (α-Cr₂O₃). Using X-ray absorption measurements, we connect the colors of the Cr _x Al_2−x O₃ series with the structural and electronic local environment around Cr. UV–VIS electronic parameters, such as the crystal field and the Racah parameter B, are related to those deduced from the analysis of the isotropic and XMCD spectra at the Cr L_2,3-edges in Cr_0.07Al_1.93O₃ and eskolaite. The Cr–O bond lengths are extracted by EXAFS at the Cr K-edge in the whole Cr _x Al_2−x O₃ (0.07≤x< 2) solid solution series. The variation of the mean Cr–O distance between Cr_0.07Al_1.93O₃ and α-Cr₂O₃ is evaluated to be 0.01₅ Å (≈1%). The variation of the crystal field in the Cr _x Al_2−x O₃ series is discussed in relation with the variation of the averaged Cr–O distances.     

Lattice vibration spectra. LXVIII. Single-crystal Raman spectra of marcasite-type iron chalcogenides and pnictides,FeX2 (X=S,Se, Te; P,As, Sb)

Single-crystal Raman spectra of marcasite-type FeS₂, FeSe₂, and FeTe₂ and loellingite-type FeP₂, FeAs₂, and FeSb₂ are presented and discussed with reference to the energies of the two X-X stretching modes v _x-x (A _g, B _1g) and the four X₂ librations Rx₂ (A _g, B _1g, B _2g, B _3g). The main results obtained are that (i) the intraionic X-X bonds of FeS₂ marcasite and FeS₂ pyrite are nearly equal in strengths (mean values of the S-S stretching modes 418 and 420 cm^-1, respectively) and (ii) the interactions of the metal ions and the dumbbell-like X₂ units increase on going from the chalcogenides to the respective pnictides and from FeS₂ marcasite to pyrite (as shown from the frequencies of the X₂ librations).     

Crystal-field spectra for blue and green diopsides synthesized in the join CaMgSi2O6-CaCrAlSiO6

Synthetic diopsides in the join CaMgSi₂O₆ CaCrAlSiO₆ have been studied by means of crystal-field theory. These diopsides are either blue or pale green in colour. The former forms at lower temperatures and the latter at higher temperatures. The optical spectra and colours can be unequivocally explained based on the assumption that Cr³⁺ions occupy both tetrahedral and octahedral sites in the diopsides. In the blue diopsides Cr³⁺ions are present in two kinds of spin state, i.e., tetrahedrally coordinated low spin and octahedrally coordinated high spin. On heating the blue diopsides, tetrahedral occupancy of chromium decreases sharply due to spin transformation from tetrahedral low spin to octahedral high spin. Above 1,160° C nearly all chromium ions are present in octahedral sites with high spin state and the diopsides become pale green in colour. Some petrogenetic applications of the resultes are discussed.     

Experimental and theoretical investigations on high-pressure phase transition of Sr2Fe2O5

Sr₂Fe₂O₅ is a typical oxygen-deficient perovskite and adopts brownmillerite phase (Ibm2, Z = 4) at ambient conditions. Its high-pressure structural behavior has been investigated by both synchrotron radiation X-ray diffraction with diamond anvil cell technique and first principles calculations. Experimental results clearly show that the brownmillerite Sr₂Fe₂O₅ transforms into a tetragonal perovskite-type phase at 12.0 GPa and room temperature, and then into a Sr₂Mn₂O₅-type phase (Pbam, Z = 2) at 23.3 GPa after high-temperature annealing. The Sr₂Mn₂O₅-type phase is stable up to at least 60 GPa and it further undergoes a reversible transition to a lower symmetry phase at 79.1 GPa and ~2,000 K. The results from theoretical calculation not only confirm that the tetragonal phase of Sr₂Fe₂O₅ is isostructural with the high-temperature structure of Ba₂In₂O₅ (I4/mcm, Z = 4), but also predict a series of phase transitions from brownmillerite phase to Ba₂In₂O₅-type phase at 6.9 GPa, and then to Sr₂Mn₂O₅-type phase at 19.7 GPa, which coincides with present experiment results. Isothermal pressure–volume relationship of the Sr₂Mn₂O₅-type phase can be well described by the Birch–Murnaghan Equation of State with V ₀ = 111.6(10) ų, B ₀ = 122(9) GPa, B ₀ ^′  = 4(fixed) experimentally and V ₀ = 115.8(3) ų, B ₀ = 92(4) GPa, B ₀ ^′  = 4(fixed) theoretically. The transition mechanism from brownmillerite to Ba₂In₂O₅-type phase is the displacement of four-coordinated Fe³⁺ ions to higher coordinated positions upon compression. In addition, a semiconductor-to-metal crossover is predicted from brownmillerite to Ba₂In₂O₅-type or Sr₂Mn₂O₅-type phase.     

The electronic structure and absorption spectrum of MnO 6 9− octahedra in manganian andalusite

The energy levels of MnO ₆ ^9? clusters, with D _4h approximated and C _2v actual symmetry of the M ₁ site of Mn³⁺-bearing andalusite, are calculated using the multiple scattering method. The energies of the electronic d-d transition of Mn³⁺ in the clusters with D _4h symmetry are calculated to be 6,000–7,000 cm^?1 (⁵ B _1g → ⁵ A _1g ), ～18,000 cm^?1 (⁵ B _1g → ⁵ B _2g ) and ～19,000 cm^?1 (⁵ B _1g → ⁵ E _g ). Apart from a splitting of the ⁵ E _g -level into two levels separated by 300–350 cm^?1, no significant changes of these transition energies are noted for the corresponding cluster with C _2v symmetry. The calculated transition energies give a good fit to the structure of the optical absorption spectra of Mn³⁺-bearing andalusites and support recent assignments of the major absorption bands observed in these spectra.     

Single-crystal EPR and DFT study of a <Superscript>VI</Superscript>Al–O<Superscript>−</Superscript>–<Superscript>VI</Superscript>Al center in jeremejevite: electronic structure and <Superscript>27</Superscript>Al hyperfine constants

Single-crystal electron paramagnetic resonance (EPR) spectra of a gem-quality jeremejevite, Al₆B₅O₁₅(F, OH)₃, from Cape Cross, Namibia, reveal an S = 1/2 hole center characterized by an ²⁷Al hyperfine structure arising from interaction with two equivalent Al nuclei. Spin-Hamiltonian parameters obtained from single-crystal EPR spectra at 295 K are as follows: g ₁ = 2.02899(1), g ₂ = 2.02011(2), g ₃ = 2.00595(1); A ₁/g _e β _e  = −0.881(1) mT, A ₂/g _e β _e  = −0.951(1) mT, and A ₃/g _e β _e  = −0.972(2) mT, with the orientations of the g ₃- and A ₃-axes almost coaxial and perpendicular to the Al–O–Al plane; and those of the g ₁- and A ₁-axes approximately along the Al–Al and Al–OH directions, respectively. These results suggest that this aluminum-associated hole center represents hole trapping on a hydroxyl oxygen atom linked to two equivalent octahedral Al³⁺ ions, after the removal of the proton (i.e., a ^VIAl–O⁻–^VIAl center). Periodic ab initio UHF and DFT calculations confirmed the experimental ²⁷Al hyperfine coupling constants and directions, supporting the proposed structural model. The ^VIAl–O⁻–^VIAl center in jeremejevite undergoes the onset of thermal decay at 300 °C and is completely bleached at 525 °C. These data obtained from the ^VIAl–O⁻–^VIAl center in jeremejevite provide new insights into analogous centers that have been documented in several other minerals.     

Calculated optical absorption spectra of Ni2+-bearing compounds

The transition energies responsible for optical absorption spectra can be obtained by crystal-field analysis, but the transition intensities are notoriously difficult to calculate. This paper examines the basic ingredients of the calculation of optical spectrum intensities. Magnetic dipole and electric quadrupole transitions intensities are evaluated, as well as the direct d(Ni²⁺) to p(O²⁻) electric dipole transitions. All these contributions are shown to be small in the optical range, so that spectral intensities are due to the mixing of odd orbitals with the Ni²⁺ 3d ⁿ states. Received: 11 November 1997 / Revised, accepted: 6 September 1999     

Correlation of irradiation-induced yellow color with the O<Superscript>−</Superscript> hole center in tourmaline

Tourmaline with the general formula XY₃Z₆(BO₃)₃Si₆O₁₈(OH,O)₃(OH,F) and the trigonal space group R3m (C_3v⁵) is known as a gemstone with great variety of colors. Some color centers are related to transition metal ions, and others to electron or hole traps. In this paper we report on a combined study using electron paramagnetic resonance (EPR), electron nuclear double resonance (ENDOR), and the optical detection of EPR (ODEPR) on a yellow color center produced by -irradiation in colorless Li-bearing elbaite tourmaline from Brazil. The color center is an O^– hole trap center, which is stabilized within the plane spanned by three Y sites, and is located in the structural channels formed by Si₆O₁₈. We suggest that two of the Y sites are substituted by ²⁷Al and the other by ^6,7Li. During the irradiation process atomic hydrogen H⁰ is also produced, which shows the same thermal stability as the hole center (250 °C). Therefore, we assign H⁰ to be the local charge compensator for the hole trap. From the ODEPR measurements we conclude that the yellow color is caused by the O^– hole center. The large negative isotropic Al superhyperfine interaction of the O^– hole trap center is consistent with a calculation of the transferred hyperfine interactions by exchange polarization supporting the proposed defect model of an O^– at the O₁ sites, whereby the O^– is relaxed into the plane formed by three Y ions.     

Anaerobic oxidation of methane in coastal sediment from Guishan Island (Pearl River Estuary), South China Sea

The concentrations of CH₄, SO₄²⁻, σCO₂ and the carbon isotope compositions of ΣCO₂ and CH₄ in the pore-water of the GS sedimentary core collected from Guishan Island (Pearl River Estuary), South China Sea, were determined. The methane concentration in the pore-water shows dramatic changes and sulfate concentration gradients are linear at the base of the sulfate reduction zone for the station. The carbon isotope of methane becomes heavier at the sulfate-methane transition (SMT) likely because of the Raleigh distillation effect; ¹²CH₄ was oxidized faster than ¹³CH₄, and this caused the enrichment of residual methane δ ¹³C and δ ¹³C-ΣCO₂ minimum. The geochemical profiles of the pore-water support the existence of anaerobic oxidation of methane (AOM), which is mainly controlled by the quality and quantity of the sedimentary organic matter. As inferred from the index of δ ¹³C-TOC value and TOC/TN ratio, the organic matter is a mix of mainly refractory terrestrial component plus some labile alga marine-derived in the study area. A large amount of labile organic matter (mainly labile alga marine-derived) is consumed via the process of sedimentary organic matter diagenesis, and this reduces the amount of labile organic matter incorporated into the base of the sulfate reduction zone. Due to the scarcity of labile organic matter, the sulfate will in turn be consumed by its reaction with methane and therefore AOM takes place. Based on a diffussion model, the portion of pore-water sulfate reduction via AOM is 58.6%, and the percentage of ΣCO₂ in the pore-water derived from AOM is 41.4%. Thus, AOM plays an important role in the carbon and sulfur cycling in the marine sediments of Pearl River Estuary.     

Raman spectroscopy and heat capacity measurement of calcium ferrite type MgAl2O4 and CaAl2O4

Raman spectroscopy of calcium ferrite type MgAl₂O₄ and CaAl₂O₄ and heat capacity measurement of CaAl₂O₄ calcium ferrite were performed. The heat-capacity of CaAl₂O₄ calcium ferrite measured by a differential scanning calorimeter (DSC) was represented as C_P(T)=190.6–1.116 × 10⁷T^–2 + 1.491 × 10⁹T^–3 above 250 K (T in K). The obtained Raman spectra were applied to lattice dynamics calculation of heat capacity using the Kieffer model. The calculated heat capacity for CaAl₂O₄ calcium ferrite showed good agreement with that by the DSC measurement. A Kieffer model calculation for MgAl₂O₄ calcium ferrite similar to that for CaAl₂O₄ calcium ferrite was made to estimate the heat capacity of the former. The heat capacity of MgAl₂O₄ calcium ferrite was represented as C_P(T)=223.4–1352T ^–0.5 – 4.181 × 10⁶T ^–2 + 4.300 × 10⁸T ^–3 above 250 K. The calculation also gave approximated vibrational entropies at 298 K of calcium ferrite type MgAl₂O₄ and CaAl₂O₄ as 97.6 and 114.9 J mol^–1 K^–1, respectively.     

High-pressure transitions and thermochemistry of MGeO3 (M=Mg, Zn and Sr) and Sr-silicates: systematics in enthalpies of formation of A2+B4+O3 perovskites

Phase transitions in MgGeO₃ and ZnGeO₃ were examined up to 26 GPa and 2,073 K to determine ilmenite–perovskite transition boundaries. In both systems, the perovskite phases were converted to lithium niobate structure on release of pressure. The ilmenite–perovskite boundaries have negative slopes and are expressed as P(GPa)=38.4–0.0082T(K) and P(GPa)=27.4−0.0032T(K), respectively, for MgGeO₃ and ZnGeO₃. Enthalpies of SrGeO₃ polymorphs were measured by high-temperature calorimetry. The enthalpies of SrGeO₃ pseudowollasonite–walstromite and walstromite–perovskite transitions at 298 K were determined to be 6.0±8.6 and 48.9±5.8 kJ/mol, respectively. The calculated transition boundaries of SrGeO₃, using the measured enthalpy data, were consistent with the boundaries determined by previous high-pressure experiments. Enthalpy of formation (ΔH _f°) of SrGeO₃ perovskite from the constituent oxides at 298 K was determined to be −73.6±5.6 kJ/mol by calorimetric measurements. Thermodynamic analysis of the ilmenite–perovskite transition boundaries in MgGeO₃ and ZnGeO₃ and the boundary of formation of SrSiO₃ perovskite provided transition enthalpies that were used to estimate enthalpies of formation of the perovskites. The ΔH _f° of MgGeO₃, ZnGeO₃ and SrSiO₃ perovskites from constituent oxides were 10.2±4.5, 33.8±7.2 and −3.0±2.2 kJ/mol, respectively. The present data on enthalpies of formation of the above high-pressure perovskites were combined with published data for A²⁺B⁴⁺O₃ perovskites stable at both atmospheric and high pressures to explore the relationship between ΔH _f° and ionic radii of eightfold coordinated A²⁺ (R _A) and sixfold coordinated B⁴⁺ (R _B) cations. The results show that enthalpy of formation of A²⁺B⁴⁺O₃ perovskite increases with decreasing R _A and R _B. The relationship between the enthalpy of formation and tolerance factor ( R _o: O²⁻ radius) is not straightforward; however, a linear relationship was found between the enthalpy of formation and the sum of squares of deviations of A²⁺ and B⁴⁺ radii from ideal sizes in the perovskite structure. A diagram showing enthalpy of formation of perovskite as a function of A²⁺ and B⁴⁺ radii indicates a systematic change with equienthalpy curves. These relationships of ΔH _f° with R _A and R _B can be used to estimate enthalpies of formation of perovskites, which have not yet been synthesized.     

Optical spectroscopic study of synthetic NaScSi<Subscript>2</Subscript>O<Subscript>6</Subscript>–CaNiSi<Subscript>2</Subscript>O<Subscript>6</Subscript> pyroxenes at normal and high pressures

Six synthetic NaScSi₂O₆–CaNiSi₂O₆ pyroxenes were studied by optical absorption spectroscopy. Five of them of intermediate (Na_1−x , Ca _x )(Sc_1−x , Ni _x )Si₂O₆ compositions show spectra typical of Ni²⁺ in octahedral coordination, more precise Ni²⁺ at the M1 site of the pyroxene structure. The common feature of all spectra is three broad absorption bands with maxima around 8,000, 13,000 and 24,000 cm⁻¹ assigned to ³ A _2g → ³ T _2g, ³ A _2g → ³ T _1g and →³ T _1g (³ P) electronic spin-allowed transitions of ^VINi²⁺. A weak narrow peak at ∼14,400 cm⁻¹ is assigned to the spin-forbidden ³ A _2g → ¹ T _2g (¹ D) transition of Ni²⁺. Under pressure the spin-allowed bands shift to higher energies and change in intensity. The octahedral compression modulus, calculated from the shift of the ³ A _2g → ³ T _2g band in the (Na_0.7Ca_0.3)(Sc_0.7Ni_0.3)Si₂O₆ pyroxene is evaluated as 85±20 GPa. The Racah parameter B of Ni²⁺(M1) is found gradually changing from ∼919 cm⁻¹ at ambient pressure to ∼890 cm⁻¹ at 6.18 GPa. The Ni end-member pyroxene [(Ca_0.93 Ni_0.07)NiSi₂O₆] has a spectrum different from all others. In addition to the above mentioned bands of Ni²⁺(M1) it displays several new relatively intense and broad extra bands, which were attributed to electronic transitions of Ni²⁺ at the M2 site. In difference to CaO₈ polyhedron geometry of an eightfold coordination, Ni²⁺(M2)O₈ polyhedra are assumed to be relatively large distorted octahedra. Due to different distortions and different compressibilities of the M1 and M2 sites the Ni²⁺(M1)- and Ni²⁺(M2)-bands display rather different pressure-induced behaviors, becoming more resolved in the high-pressure spectra than in that measured at atmospheric pressure. The octahedral compression modulus of Ni²⁺(M1) in this end-member pyroxene is evaluated as 150 ± 25 GPa, which is noticeably larger than in Ni_0.3 pyroxene. This is due to a smaller size and, thus, a stiffer character of Ni²⁺(M1)O₆ octahedron in the (Ca_0.93Ni_0.07)NiSi₂O₆ pyroxene compared to (Na_0.7Ca_0.3)(Sc_0.7Ni_0.3)Si₂O₆.

A theoretical investigation of the relative stabilities of Fe-free clinozoisite and orthozoisite

 The relative stabilities of orthozoisite, Ca₂Al₃[O|OH|Si₂O₇|SiO₄], space group Pnma, and the monoclinic polymorph, clinozoisite, space group P2₁/m, have been investigated using calculations based on density functional theory. It is found that orthozoisite is more stable than clinozoisite by about 1 kJ mol⁻¹ at zero pressure in the athermal limit. The bulk moduli of the two polymorphs have been calculated to be B_ortho=117.5(1.7) GPa and B_clino=136(4) GPa. Received: 20 March 2000 / Accepted: 26 February 2001     

Polarized electronic absorption spectra of synthetic (Mg,Fe)-orthopyroxenes,ferrosilite and Fe3+-bearing ferrosilite

The assignment of spin-allowed Fe²⁺-bands in orthopyroxene electronic absorption spectra is revised by studying synthetic bronzite (Mg_0.8 Fe_0.2)₂Si₂O₆, hypersthene (Mg_0.5 Fe_0.5)₂Si₂O₆ and ferrosilite (Fe₂Si₂O₆). Reheating of bronzite and hypersthene single crystals causes a redistribution of the Fe²⁺-ions over the M1 and M2 octahedra, which was determined by Mössbauer spectroscopy and correlated to the intensity change of the spin-allowed Fe²⁺ d-d bands in the polarized absorption spectra. The 11000 cm^-1 band is caused by Fe²⁺ in M1 (⁵B_2g→⁵A_1g) and Fe²⁺ in M2 (⁵A₁→⁵A₁), the 8500 cm^-1 band by Fe²⁺ in M1 (⁵B_2g→⁵B_1g) and the 5000 cm^-1 band by Fe²⁺ in M2 octahedra (⁵A₁→⁵B₁). The Fe²⁺-Fe³⁺ charge transfer band is identified at 12500cm^-1 in the spectra of synthetic Fe³⁺ -Al bearing ferrosilite. This band shows a strong γ-polarization and therefore is caused by Fe²⁺ -Fe³⁺-ions in edge-sharing octahedra.